The X (2)Pi and A (2)Sigma (+) electronic states of HCN+ have been studied using a previously developed method [Carter , Mol. Phys. 98, 1967 (2000)] suitable for triatomic molecules showing three-state (Renner-Teller+vibronic) interactions. Ab initio three-dimensional diabatic potential energy surfaces for the (2)Pi (1 (2)A',1 (2) A') and (2)Sigma (+)(2 (2)A') states have been computed at the multireference configuration interaction level of theory, using extended Gaussian basis sets. Additional computations were done to determine the barrier to isomerization over the three surfaces and the spin-orbit constant for the (2)Pi state. Energies, spin-orbit splittings, and rotational constants have then been calculated for all rovibronic levels of Sigma and Pi symmetry up to 5800 cm(-1) for HCN+ and 4800 cm(-1) for DCN+. Assignments based on plots of vibrational wave functions are also provided. These computations have been finally used to revise previous interpretations of photoelectron spectra.